Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D293 |
| Fitting | C32×C293 ⋊ C2 |
| derived, Sylow | C293 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D293 |
| commutator, hypocenter | C293 | C2×C32 |
| Frattini | C16 | C2×D293 |
| Fitting | C32×C293 | C2 |
| socle | C2×C293 | C2×C16 |
| prime radical | C2×D293 | C16 |
| cosocle | C16×C293 | C22 |
| LCS | G ▷ C293 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
4736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D293, #49156995, C2×C32×D293, … |
| maximal normal subgroup of | C64×D293, #49156995, C2×C32×D293, … |
| maximal quotient of | C32×Dic293, #49156922, #49156980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 380);